Einstein, Podolsky and Rosen

Bell s Theorem In a celebrated 1935 paper, Einstein, Podolsky and Rosen (EPR) [ein35] argued that quantum mechanics provides an essentially incomplete description of reality unless hidden variables exist. 

The progress undergone in recent years toward a solution of the problem raised by Einstein 1927 has become possible because of two developments (1) A few experimental techniques, in particular, the methods for measuring very short times with good accuracy, have permitted in recent years the execution of several experiments which in their essence are practical versions of the thought experiment proposed and discussed in 1935 by Einstein, Podolski, and Rosen.39 (2) A procedure of analysis of their results has been made possible by the work of Bell40 who has derived in the frame of local realism a relation (the Bell inequality) obeyed by local realistic theories but violated by quantum mechanics. 

A. Afriat and F. Selleri, The Einstein, Podolsky and Rosen Paradox in Atomic, Nuclear and Particle Physics, Plenum, New York, 1998. 

Einstein, Podolsky and Rosen (EPR) [Einstein 1935] asked the question of whether the quantum mechanical description of physical world is complete, giving the following example. Two-particles are in the quantum state showing strange correlations if one measures the position or momentum of one particle, one can predict with certainty the result of measuring their counterpart for the second particle. Thus, depending on which measurement is chosen for the first particle, the value of either the momentum or position can be predicted with arbitrary precision for the other particle. The later discussion has concerned the interpretation of the EPR paradox and its implications on quantum theory [Bohr 1935], Later, Bohm considered [Bohm 1951] two entangled spin-1/2 particles, which have become the center of attention on this EPR issue their... 

Ever since Einstein, Podolsky, and Rosen in their seminal paper from 1935 [Einstein 1935] introduced the possibility of entangling two quantum system, entanglement has been viewed as one the most curious and spectacular phenomena in quantum mechanics. In the past few years the role of entanglement in quantum mechanics has shifted dramatically from being a fundamental test of the foundation of the entire quantum mechanical theory to being a techni-... 

The above mentioned paper by Einstein, Podolsky, and Rosen represented a severe critique of quantum mechanics in the form that has been presented by its fathers. After its publication, Erwin Schrddinger published a series of works showing some other problematic issues in quantum mechanics. In particular, he described a Gedanken experiment, later known as the Schrddinger s cat paradox. According to Schrddinger, this paradox shows some absurd consequences of quantum mechanics. 

Aftiat A, Seller F (1999) The Einstein, Podolsky, and Rosen paradox in atomic, nuclear, and particle physics. Plenum Press, New York McWeeny R (2000) Adv Quant Chem 36 365 Head-Gordon M (2003) Chem Phys Lett 372 508... 

Ib honour Einstein, Podolsky and Rosen the entanglement of states is sometimes called the EPR effect. 

The polarization correlation in two-photon processes has thus proved a topic of considerable interest in its own right. However, without doubt, the main stimulus to the performance of polarization correlation measurements came first from the Gedankenexperiment of Bohm and the paper of Bohm and Aharonov in which the so-called paradox of Einstein, Podolsky, and Rosen (EPR) was put in terms of the polarization of photons and subsequently from the work of Bell and its interpretation in experimental terms by Clauser, Home, Shimony, and Holt, and Clauser and Home. ... 

Quantum mechanics tells us that, before observation is made, both spins share - with equal weight - the states 11> and ].). Before a measurement, the probability of either spin to be found in either state is 50%. However, if one performs a measurement, say, in first spin, the state of the second spin becomes determined, no matter the distance between them For many years, this non-local property of entanglement has been perhaps the most controversial and debated aspect of quantum mechanics, since Einstein, Podolsky and Rosen pointed the problem out in a historical paper published in 1935 [13]. Since the EPR paper, as it became known, many decades were necessary until the discovery of a criterion to decide whether non-locality was a physical reality or just a mathematical property of the quantum formalism. This was a main contribution of John Bell, who in 1964 presented such a criterion [14]. The so-called Bell inequality is a statistical test for quantum nonlocality. However, in 1964 there were no experimental conditions to implement such a test in a real physical system. This came about only in 1982 as a seminal work published by Aspect, Grangier and Roger [15], entitled Experimental realization of Einstein-Podolsky-Rosen-Bohm gedankenexperiment a new violation of Bell s inequalities. This paper is considered - at least for the great majority of physicists - as the work where the nonlocality, inherent to entangled states, is demonstrated to be definitely part of the physical world. 

Although Bohm formalism provides the most forceful demonstration of the non-local character of quantum theory, the evidence has been around for many decades. The so-called EPR effect was first recognized by Einstein and his co-workers, Podolsky and Rosen in 1935 [3]. The purpose of their work was to demonstrate that the apparent non-local nature of quantum mechanics could only mean that a vital element was missing from the theory. The missing element had to be such as to counteract the non-local feature. 

While this above state of affairs is decidedly counterintuitive, it has the virtue of simply and easily - at least in principle - accounting for one of the deep mysteries of quantum mechanics namely, an apparent noidocality as expressed by the Einstein-Podolsky-Rosen gcdarikcn experiment [ein35] and Bell s theorem [bell64] (see discussion box). Finite nature implies that any system that is allowed to evolve from some distant initial state possesses causality in all space-time directions. This implies, in particular, that no part of space can be considered to be causally separated from another, and that therefore the DM universe will always harbor effects that cannot be attenuated by distance. 

The second axiom, which is reminiscent of Mach s principle, also contains the seeds of Leibniz s Monads [reschQl]. All is process. That is to say, there is no thing in the universe. Things, objects, entities, are abstractions of what is relatively constant from a process of movement and transformation. They are like the shapes that children like to see in the clouds. The Einstein-Podolsky-Rosen correlations (see section 12.7.1) remind us that what we empirically accept as fundamental particles - electrons, atoms, molecules, etc. - actually never exist in total isolation. Moreover, recalling von Neumann s uniqueness theorem for canonical commutation relations (which asserts that for locally compact phase spaces all Hilbert-space representations of the canonical commutation relations are physically equivalent), we note that for systems with non-locally-compact phase spaces, the uniqueness theorem fails, and therefore there must be infinitely many physically inequivalent and... 

This bizarre prediction, known as the Einstein-Podolsky-Rosen paradox, has been verified many times in the laboratory. The most famous version involves two electrons manipulated into a mixed state with combined spin of 0, The electrons are separated in space before the spin of one (and only one) electron is measured, say, in a Stern-Gerlach machine. If that electron is found to be spin up, then by conservation of spin angular momentum, the other electron must be spin down, and vice versa. This holds true even if the ratio of the distance between the measurements to the time between the measurements is greater than the speed of light. See the discussion in Townsend [To, Sections 5,4 and 5,5] and the references therein. 

A. Einstein, B. Podolski, and N. Rosen, Phys. Rev. 47, 111 (1935) F. Selleri ed., Quantum Mechanics Versus Local Realism - The Einstein-Rosen-Podolski Paradox (Plenum, New York 1988). 

A. Kyprianidis and J. P. Vigier, Action-at-a-distance The mystery of Einstein-Podolsky-Rosen correlations, in F. Selleri (Ed.), Quantum Mechanics versus Local Realism The Einstein-Podolsky—Rosen Paradox, ISBN 0-30-642739-7, Plenum, New York, 1988, p. 273. 

P. R. Holland and J. P. Vigier, The quantum potential and signaling in the Einstein-Podolsky-Rosen experiment, Found. Phys. 18(7), 741-750 (1988). 

N. Cufaro-Petroni, A. Garuccio, F. Selleri, and J. P. Vigier, On a contradiction between the classical (idealized) quantum theory of measurement and the conservation of the square of the total angular momentum in Einstein-Podolsky-Rosen paradox, C. R. Acad. Sci., Ser. B (Sciences Physiques), 290(6), 111-114 (1980). 

N. Cufaro-Petroni and J. P. Vigier, Causal superluminal interpretation of the Einstein-Podolsky-Rosen paradox, Lett. Nuovo Cimento 26(5) (Ser. 2), 149-154 (1979). 

This chapter is organized as follows In Section 2, quantum states are briefly described. Section 3 presents aspects of standard quantum measurement model. Section 4 includes double-slit, Einstein-Podolsky-Rosen, and Tonomura s experiments. Section 5 illustrates calculations of quantum states for quantum measurements. In Section 6, atom interferometer experiment of Scully et al. is analyzed. A detailed discussion is presented in Section 7, emphasizing a physical perception of quantum mechanics. 

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